Answer
$\frac{9}{4}\pi$
Work Step by Step
On the $xy-$plane
1) $x^2+y^2\leq 9$ describes the region of all points inside the circle $x^2+y^2=9$ centered at $(0,0)$ with the radius of $3$.
2) $y\geq |x|$ describes the region of all points above the graph $y=|x|$
The region that satisfies both inequalities is given below.
Calculate the area of the region:
$\frac{1}{4}\cdot$ Area of circle $=\frac{1}{4}\cdot \pi\cdot 3^2=\frac{9}{4}\pi$
